Well, the smart thing to do woul be do buy VectorScribe. It has parametric objects, which include partial drawing of slices/ sectors. Makes this a million times easier than anything AI offers natively.

Thank you, I've downloaded it to check it out (after messing about a lot with the scissor tool and finding that the Join command is very particular about which ends to join ). If it does what I want, I'll let you know.

You can use the Polar grid but be warned you have to use more division than you need in order to combine smaller units to make larger ones and you have to increase the storke width of the dividers in order to outline them so you can use the pathfinders divide feature to then eliminate unwanted parts.And you might have to maually add a spoke or two back.It is a bit of work it would be good to have an update to the graph tool so charts like this could also be made. That is not likely to happen.

Thank you everyone who answered. Jacob helped me the most with the Object>Path>Divide Objects below, then I used Carlos's suggestion to paint the colours in. I had to do everything several times before I got a reasonable result, but that's the learning process. Also the "Divide Objects below" did not always divide properly - probably I was doing something wrong. I made some of the divided objects compound paths to make them fillable in the right direction.

I'll be able to use these techniques in other projects. I quite often get diagrams and the circular ones are the most tricky for me, though I surprise myself sometimes when get the right result from the bezier curves I drew.

I'll also look into the software suggested and have downloaded it already. It might be the easiest solution but I have to learn it first and not enough time to learn for my client's work which (being done on Easter weekend) was in overrun time.